Uncertainty in microscale gas damping: Implications on dynamics of capacitive MEMS switches

Effects of uncertainties in gas damping models, geometry and mechanical properties on the dynamics of micro-electro-mechanical systems (MEMS) capacitive switch are studied. A sample of typical capacitive switches has been fabricated and characterized at Purdue University. High-fidelity simulations o...

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Vydané v:	Reliability engineering & system safety Ročník 96; číslo 9; s. 1171 - 1183
Hlavní autori:	Alexeenko, Alina, Chigullapalli, Sruti, Zeng, Juan, Guo, Xiaohui, Kovacs, Andrew, Peroulis, Dimitrios
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Ltd 01.09.2011
Predmet:	Aleatory uncertainty Damping Dynamics Electric potential Epistemic uncertainty Impact velocity Mathematical models Microsystems Quantification of margins and uncertainties RF MEMS Squeeze-film damping Switches Uncertainty Uncertainty analysis Voltage Microsystems Epistemic uncertainty RF MEMS Quantification of margins and uncertainties Squeeze-film damping Uncertainty analysis Aleatory uncertainty
ISSN:	0951-8320, 1879-0836
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Abstract	Effects of uncertainties in gas damping models, geometry and mechanical properties on the dynamics of micro-electro-mechanical systems (MEMS) capacitive switch are studied. A sample of typical capacitive switches has been fabricated and characterized at Purdue University. High-fidelity simulations of gas damping on planar microbeams are developed and verified under relevant conditions. This and other gas damping models are then applied to study the dynamics of a single closing event for switches with experimentally measured properties. It has been demonstrated that although all damping models considered predict similar damping quality factor and agree well for predictions of closing time, the models differ by a factor of two and more in predicting the impact velocity and acceleration at contact. Implications of parameter uncertainties on the key reliability-related parameters such as the pull-in voltage, closing time and impact velocity are discussed. A notable effect of uncertainty is that the nominal switch, i.e. the switch with the average properties, does not actuate at the mean actuation voltage. Additionally, the device-to-device variability leads to significant differences in dynamics. For example, the mean impact velocity for switches actuated under the 90%-actuation voltage (about 150 V), i.e. the voltage required to actuate 90% of the sample, is about 129 cm/s and increases to 173 cm/s for the 99%-actuation voltage (of about 173 V). Response surfaces of impact velocity and closing time to five input variables were constructed using the Smolyak sparse grid algorithm. The sensitivity analysis showed that impact velocity is most sensitive to the damping coefficient whereas the closing time is most affected by the geometric parameters such as gap and beam thickness. ► We examine stochastic non-linear response of a microsystem switch subject to multiple input uncertainties. ► Sample devices have been fabricated and device-to-device variability have been measured. ► A coarse-grained model is used for coupled electrostatic, mechanical and fluidic response. ► Polynomial chaos expansion on a Smolyak sparse grid has been applied for uncertainty propagation. ► Device-to-device variability and ambient uncertainty have significant implications on actuation and impact dynamics.
AbstractList	Effects of uncertainties in gas damping models, geometry and mechanical properties on the dynamics of micro-electro-mechanical systems (MEMS) capacitive switch are studied. A sample of typical capacitive switches has been fabricated and characterized at Purdue University. High-fidelity simulations of gas damping on planar microbeams are developed and verified under relevant conditions. This and other gas damping models are then applied to study the dynamics of a single closing event for switches with experimentally measured properties. It has been demonstrated that although all damping models considered predict similar damping quality factor and agree well for predictions of closing time, the models differ by a factor of two and more in predicting the impact velocity and acceleration at contact. Implications of parameter uncertainties on the key reliability-related parameters such as the pull-in voltage, closing time and impact velocity are discussed. A notable effect of uncertainty is that the nominal switch, i.e. the switch with the average properties, does not actuate at the mean actuation voltage. Additionally, the device-to-device variability leads to significant differences in dynamics. For example, the mean impact velocity for switches actuated under the 90%-actuation voltage (about 150 V), i.e. the voltage required to actuate 90% of the sample, is about 129 cm/s and increases to 173 cm/s for the 99%-actuation voltage (of about 173 V). Response surfaces of impact velocity and closing time to five input variables were constructed using the Smolyak sparse grid algorithm. The sensitivity analysis showed that impact velocity is most sensitive to the damping coefficient whereas the closing time is most affected by the geometric parameters such as gap and beam thickness. Effects of uncertainties in gas damping models, geometry and mechanical properties on the dynamics of micro-electro-mechanical systems (MEMS) capacitive switch are studied. A sample of typical capacitive switches has been fabricated and characterized at Purdue University. High-fidelity simulations of gas damping on planar microbeams are developed and verified under relevant conditions. This and other gas damping models are then applied to study the dynamics of a single closing event for switches with experimentally measured properties. It has been demonstrated that although all damping models considered predict similar damping quality factor and agree well for predictions of closing time, the models differ by a factor of two and more in predicting the impact velocity and acceleration at contact. Implications of parameter uncertainties on the key reliability-related parameters such as the pull-in voltage, closing time and impact velocity are discussed. A notable effect of uncertainty is that the nominal switch, i.e. the switch with the average properties, does not actuate at the mean actuation voltage. Additionally, the device-to-device variability leads to significant differences in dynamics. For example, the mean impact velocity for switches actuated under the 90%-actuation voltage (about 150 V), i.e. the voltage required to actuate 90% of the sample, is about 129 cm/s and increases to 173 cm/s for the 99%-actuation voltage (of about 173 V). Response surfaces of impact velocity and closing time to five input variables were constructed using the Smolyak sparse grid algorithm. The sensitivity analysis showed that impact velocity is most sensitive to the damping coefficient whereas the closing time is most affected by the geometric parameters such as gap and beam thickness. ► We examine stochastic non-linear response of a microsystem switch subject to multiple input uncertainties. ► Sample devices have been fabricated and device-to-device variability have been measured. ► A coarse-grained model is used for coupled electrostatic, mechanical and fluidic response. ► Polynomial chaos expansion on a Smolyak sparse grid has been applied for uncertainty propagation. ► Device-to-device variability and ambient uncertainty have significant implications on actuation and impact dynamics.
Author	Zeng, Juan Peroulis, Dimitrios Chigullapalli, Sruti Kovacs, Andrew Alexeenko, Alina Guo, Xiaohui
Author_xml	– sequence: 1 givenname: Alina surname: Alexeenko fullname: Alexeenko, Alina email: alexeenk@purdue.edu organization: School of Aeronautics & Astronautics, Purdue University, West Lafayette, IN 47907, United States – sequence: 2 givenname: Sruti surname: Chigullapalli fullname: Chigullapalli, Sruti organization: School of Aeronautics & Astronautics, Purdue University, West Lafayette, IN 47907, United States – sequence: 3 givenname: Juan surname: Zeng fullname: Zeng, Juan organization: School of Electrical & Computer Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, United States – sequence: 4 givenname: Xiaohui surname: Guo fullname: Guo, Xiaohui organization: School of Aeronautics & Astronautics, Purdue University, West Lafayette, IN 47907, United States – sequence: 5 givenname: Andrew surname: Kovacs fullname: Kovacs, Andrew organization: School of Electrical & Computer Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, United States – sequence: 6 givenname: Dimitrios surname: Peroulis fullname: Peroulis, Dimitrios organization: School of Electrical & Computer Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, United States
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SubjectTerms	Aleatory uncertainty Damping Dynamics Electric potential Epistemic uncertainty Impact velocity Mathematical models Microsystems Quantification of margins and uncertainties RF MEMS Squeeze-film damping Switches Uncertainty Uncertainty analysis Voltage
Title	Uncertainty in microscale gas damping: Implications on dynamics of capacitive MEMS switches
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